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-31-
,II ,( I
'j (IV !,' tll\·J
"lie.. or~ \(\-te4es·t-e_d ir) '-these rl()~5 +hCAr'I KsQ..p~r\c~ti(H'\S 1n eu oc - COf ce c...+l V)~ codes.~,dd F ot tO~~.?iC\e.V\+s will be- -I,ll ,fe,
------------ ---------------------------,Be uJ.f4-e. _ _ _ _ ___ Qor:/+ COy}~!Jse. pD\j-Y1oyY)[ais ~+~ -lvl"lcA-iO'ls.
For ev. (AWl p)~ ,I oak. at _{ltl:::- )\2+-'1-+\ f Z::s ex]3 ts.) z: _i 4 + f.- -\-\ __ G_ 723 C)(..J,_
- -No T e. -I-'\-) O-.{ _ ihe.se. d..- poJU!'} om i0.b. (~P v e seVlt f-h e
5CAVY1e _{ul/lcHo., - _eue.vL .:\--'hovBL +1t1~ ;) pol(J VLol'VllGlLsOtV"e. ctlfte.V'el'lt. The ~ C~'2.
X +- 'L'I.. +- \i?.\- 2..
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audreyRectangle
50 ) ,'II 123 ex)
(x3~2 )( )(2+ 2)(+\) ==
~ ::: ~\e.\d?()() t f [~J o~~b() z: 0(1-) ~ tx)
\ fV\ pI ies e(+herpolat'lotv\t4-\) ,
ded,ee 70 t'> r( fed u.," 6 \et01 ~(-t)) hL't-) ~ F [)()
~ ('I.) Or ~l',C) Is o~ de(r~e.. 0
tio~: P-[)(J ~s vtrd- YY)Ue-h l;I~€- ?Lt-he u\'\,-Ls os« +he- ()OY)-O ) coV\S+~J.'\+ \,o~>'\ovv\lGl.h,The.- p"'lrY1eS (A.'re.. the.. i(r~duLlb\e pol(t noW\.ia.,\S.
lE~~mEI;J ~ lrved"Liule paid I')Or>1ia.\:- 'i"~2 [x?]»:-------~
~(ee. iJ (-f.) t:V 13.+1, ose: i((tdu
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Wh lch (JfTo ~V\.5we..rfutA.t .for
(X-q) di\[i-d;s_- ~l'J-)~ Z:2 ['Jl] C==) -4-(~) = 0,We.. pCCI va. -\:;.h t SilL VL {ew -f "'d-es J_
)' ~o 1(\f-) o~ dt~!'e.e. j veduG-lbL #_~~4-S__ _ --l ::. X,'I'J.. _X ;, 4- X ::: X ('I.. '2.+- \ ) _ _ __ _X ') 1- 'f.. 'L =- '/..2- ( X +I ) _ _X34-x'L4-x+-t _ (x+\)(X2~\)X 3 +- X 'Lt- '( -= X ('/.. 'l.+- X ;- I )
WhoJ Q~Ji't);- )(3 +- \ _~l~)::: X o3.f-~;- ~+tf- ) ~ )( :3±:- :('"2.--\- \
redu tt ~ \eirudyc.i b iei(f'1...C\ut.\ ble!-~-~ ..\~
0_ +he OVIh :c.c
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1(\ 6f de, -h> v. de r,sra •..•c.I po \~ ~o:"i '11 ti nv 5 E[~] )_lAJhen~ F::c {-I'e.j~J (,{)t ()e..ed +he d I VISIOn ~\Vout~.'I1ten uJe. w \ \\ be. o.b Ie. 1-0 pro ve: po '0 no ~il .Q,.!
ve}rs<~>< -rJ~~ -\-i
=01- ~ ,~I'YlCL(nd ef'
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o: () d j- L,dr ('I.. ) C\()d
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.---------~------------------.---------r--- ~ . .{ ,,(j "F_ld ) de ru ~ 0= n ~
1J)() hGts OIA mos+ YL Y-oo+s co(}V\f'n~rnv It,p II r.i +-:1 (Th 15 mettl'lS & -\J~ h45 d ro 0 tstoun+tn~ i +coic e, ), _
Proo~~ Cof" 0 II CA. v:d \) {l Q) = 0 -"> {( t- ) = (x. -Q) d-L)(J .
Here. de.~ ~ = de(j a +1 ~ cle.j ~ ::. deo ~ - I.:;0 vUe.- 4-1() ish --\-he pr-otJ ~ '0(} I' ndv t:.-.t( 6.,. Orl+he- ck~'''-'' at .f. !Ill~-~--~------~~~----~-.......... ..---'
CorD \\ ~"O 3 [vt-('~ ,v\eo.l LV' ~ [x J lS pr(nc'p~L"roo
-
d~~vee,
I ~l~l•f [xJtto
- ----
• <
Thi5 means eu~v-~ a (:- (2F 15 0..(x: f-I_ I). T~u5 (x-o,) d;uiC\es
~Y- oJ\ GL E. VCr) /VI 0 re. 0 ae»:( X - fA.) #cV) cJ lx - b )
(lh ,e.\a-\-\o-eid prime. poid>1orYliais i~ 1A(e,'B~ + +-he. \e.c.ui (0e-t-~\Gl
> • -41-
c--------'\h'rf\ t 'p [)() €: F Lx] \ >
- p ('l ) I ("'( e. d u C-.l ~ t e # < p(){) z: W) a x i V11c.J icfC',d i h F[" Jprcoj- l savVle OlS {of -Z)
C£5pld i irec\vc-(I.a\e.. I:: [deal il'1 F [x] such +~tt+
~ t{ el d uJ,~h
----- ------- --- 45 -
fF'/j =- 22-;L~ )(3 1-)( + \>l h e e\ements. o~ lf9 ClAn be.. viewe-d ascA...~ Q.o-tQ\E1 +Qa..e2 ) cld t 2Zd.
G o: 'loot o{. X3+- 't + \ -= 0 I __ .---~- .•- ___----.-----,.,,-_:.0 ".."..---
..
-r
Lqj\! ~ =- G'~ (~){n c G oJo l s i-,-eldf------------ ~
~N()t~ +hcd -Czo +a,1d ~ .;; -: r(e) 3 )1.6_ A folMrlOWlia\ o~ .de~(e~ < 3 z, de8ree(x+~+' ,
Thus #1e. ~\evrJ~v1ts rL>c) ~ p,ef.e!1+ +he.-\,erY1CA.\nOers of -p-o\G()Q~~Cd5 in Zl2 L,e]urn div'I&i()" _b~ X 3->-)(+ I.
\\-.15 is OlYla.loqOllS -Iv ~~»iVld ~3 ZCO Y1S \ S t-5 0t- 0 Y~VY) at ytd ers4- inteoers upon ~11I15Id'" 10;1- '163.
peo~ \esr-o.nd 5
-------------------~-"'--------------~-- ..•.\~~. :"- -leno.,) olhl
.,
~--o~ 'F'OvJU~,,__ 6Q83 -\- e -\-\ ==- 0 =?J e3z: - e - \ = e 4- \
o.S -\ = \ C vYlDd ;()
(~ 2 3
t1 "a 0 -t- (\6 --\-i'J.2- e)::. a: 0 (j +- a I e + Q2- -0- Qoe + Q, e'2-+ Q2( G +-\)..., Q ~ + (9.0 +- Q2 ) e + 0.. \ e '2
So MU\t;pliclA.-hol')(oe. ~~\ (\ et/\ fs
(qO) u, ) q~) 7Th~5 ~e~d b k1 [S CL ~L S ( Yc1jf (5 e.r,
r . . --F-\em en ~ ot \f'1 , "'"CAo \ 0..\ az'\~,I
G 0 { 0- -6'2 0 0, -1
I 83 I ~,- 0.84 0" I ,te5 l. , ' 1e' I ' 0 1.
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